CS473ug Head Banging Session #3 9/19/06 - 9/21/06 1. Championship Showdown What excitement! The Champaign Spinners and the Urbana Dreamweavers have advanced to meet each other in the World Series of Basketweaving! The World Champions will be decided by a best of 2 n-1 series of head-to-head weaving matches, and the ﬁrst to win n matches will take home the coveted Golden Basket (for example, a best-of-7 series requires four match wins, but we will keep the generalized case). We know that for any given match there is a constant probability p that Champaign will win, and a subsequent probability q = 1-p that Urbana will win. Let P ( i,j ) be the probability that Champaign will win the series given that they still need i more victories, whereas Urbana needs j more victories for the championship. P (0 ,j ) = 1, 1 ≤ j ≤ n , because Champaign needs no more victories to win. P ( i, 0) = 0, 1 ≤ i ≤ n , as Champaign cannot possibly win if Urbana already has. P (0 , 0) is meaningless. Champaign wins any particular match
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